000013-beauty-days-at-the-movie

Beautiful Days at the Movies

Lily likes to play games with integers. She has created a new game where she determines the difference between a number and its reverse. For instance, given the number 12, its reverse is 21. Their difference is 9. The number 120 reversed is 21, and their difference is 99.

She decides to apply her game to decision making. She will look at a numbered range of days and will only go to a movie on a beautiful day.

Explain 1

[in]
20 23 6

[out]
2

Lily may go to the movies on days 20, 21, 22, and 23. We perform the following calculations to determine which days are beautiful:

• Day 20 is beautiful because the following evaluates to a whole number:
  • | 20 - 02 | / 6 = 18 / 6 = 3
• Day 21 is not beautiful because the following doesn't evaluate to a whole number:
  • | 21 - 12 | / 6 = 9 / 6 = 1.5
• Day 22 is beautiful because the following evaluates to a whole number:
  • | 22 - 22 | / 6 = 0 / 6 = 0
• Day 23 is not beautiful because the following doesn't evaluate to a whole number:
  • | 23 - 32 | / 6 = 9 / 6 = 1.5

Only two days, 20 and 22, in this interval are beautiful. Thus, we print 2 as our answer.